1. Field of the Invention
The present invention is related to the construction of acoustic radiators, both active speakers and passive radiators, and more specifically acoustic radiators having a diameter that is at least as large as the enclosure opening to which the radiator mounts thus allowing the use of a smaller enclosure than the prior art for the same capacity radiator.
2. Description of the Prior Art
The sound particularly from sub-woofer speakers suffers from the speaker and driver lacking the ability to move large distances to produce reasonable sound pressure levels at lower frequencies. The lower the frequency to be reproduced, the more that limitation affects the sound from the speaker. Speaker designers have tried many ways to improve the low frequency roll off to enhance the ability of the speaker to reproduce lower frequencies. Many of the prior art techniques employed by speaker designers to increase the low frequency response of the speakers often required larger and deeper enclosures to accommodate the larger speaker configurations. When the desire to improve efficiency was a factor, the designers of prior art speakers resorted to the use of larger enclosures along with larger speaker drivers. Some prior art speakers also relied on a long excursion driver as a means of maximization of the volume of air that the particular speaker moved. Other prior art low frequency speaker designs, to provide more sound output, rely on more driver piston area or more driver excursion, or both.
All prior art speaker designs follow a conventional construction design that include a resilient suspension diaphragm (i.e., surround) that encircles and connects to the outer diameter of a rigid speaker cone that is driven at the center by the driver (i.e., voice coil). In this construction configuration, the outer circumference of the surround attaches to the speaker frame (i.e., basket) and extends inward from the circumference of the basket resulting in the speaker cone having a diameter that is significantly less than the outer diameter of the basket. Thus the area of the speaker cone is always smaller than the are of the mouth of the speaker basket by about 20 to 30% in area profile. Additionally, the speaker cone of the prior art speakers is moved from a rest position inward and outward, thus the speaker cone on the inward strokes moves into the enclosure and displaces some of the enclosure air volume.
Conventional speakers are constructed as illustrated in the simplified cross-sectional diagram of FIG. 1. The conventional speaker design includes a speaker enclosure 2 with the outer diameter flange of speaker basket 4 attached to the mouth of enclosure 2. Below, and mounted to the bottom of basket 4, is permanent magnet 6 with voice coil 8 free to ride up and down the center magnetic poles, through a central hole defined by the bottom of basket 4 in response to electrical signals applied to the coils of voice coil 8 by an amplifier (not shown). The center of cone 12 is attached to the portion of voice coil 8 that extends above frame 4 and the outer diameter of cone 12 that extends toward the open mouth of enclosure 2 has affixed thereto an inner flange 18 of surround 14. Surround 14, as shown in FIG. 1, has a semi-circular cross-section, half donut shape, that extends outward from the mouth of enclosure 2, and has a second flange 16 extending outward from the half donut shape of surround 14 which is attached to outer flange of basket 4 and mouth of enclosure 2. Additionally, the conventional speaker includes a flexible spider 10, and is shown here having an optional inner cone face 12′.
Typically, the surround is made from a half circle, half donut shaped elastic material (e.g., rubber, foam, polyester, or cloth). The maximum sound pressure level from a speaker is directly proportional to the volume of air moved, with the volume of air moved being equal to the area of the cone times the excursion, or the stroke, of the voice coil. As shown in FIG. 1 for a conventional speaker, the surround suspension extends toward the center of the enclosure mouth resulting in the speaker cone being significantly smaller than the mouth of the enclosure thus compromising the piston area, or the working area, of the speaker. It can thus be seen that the longer the stroke of the voice coil, the wider (i.e., larger half circle diameter) the surround must be which even further compromises the working area of the speaker.
FIG. 2 illustrates the flexing of surround 14 as cone 12 is driven. Cone 12 is shown in two different positions, 12a being the relaxed position, and 12b being the maximum outward driven position with the distance between those positions being Xmax. Also shown is a designation of the cone diameter, Cd, which is discussed further below. Three profiles of surround 14 are also shown with 14a being the profile with cone 12 in the relaxed position, and 14b corresponding to cone in the maximum outward driven position. From FIG. 2 it can be seen that in the maximum outward driven position, the profile of surround 14b is nearly a straight line. In the relaxed profile, surround 14a is a half circle, then the length of the outside surface of surround 14 is (πD)/2, where D is the diameter of the surround profile. To tie the size of the surround to the maximum stroke of the speaker, an approximation can be made by considering the profile of the surround in the maximum stoke position to be a straight line and the relationship of the diameter D to Xmax can be seen from the triangular relationship between the measurements in the lower left of FIG. 2. Using that triangular geometry it can be seen that:((πD)/2)2=D2+Xmax2and solving that equation yields the following:2.47D2−D2=Xmax2, or 1.47D2=Xmax2
This relationship Is a good approximation of the geometrical relationship between the surround diameter and the maximum excursion of the speaker. Speaker designers typically increase the computed diameter based on a certain maximum excursion by 15%.
Therefore, for a speaker having a maximum excursion of 1 inch each way, using the above calculated result yields:
1.47D2=12; or 1.47D2=1; D=(1/1.47)½=0.824 inches for a maximum excursion of ±1 inch from rest for the cone. Now, by adding the recommended 15% to the resultant value for D, i.e., 1.15D=1.15×0.824=0.947 inches, or about one inch. Note, that for the 1 inch example above, the diameter of the cone, Cd will be approximately 2 inches less than the diameter of the mouth of the enclosure. It is not believed that speaker designers knew about these simple relationships; instead the prior designs have been based on the conventional wisdom in the industry, not mathematics.
Since the mathematical relationship disclosed above was not previously known, the volume of air moved by the speaker to the maximum excursion was also unknown. Again referring to FIG. 2, the volume of air moved can be seen to be represented mathematically by the following equation:V=(⅙)πXmax[(3CD2/4)+3D2+(6CDD/2)+(3CD2/4)+Xmax2]which reduces toV=(⅙)πXmax[(3CD2/2)+3D2+3CDD+Xmax2]
Using a typical 12 inch woofer, D=1.7 inches, Cd=7.5 inches and Xmax=1.5 inches,
                    V        =                ⁢                              (                          1.5              /              6                        )                    ⁢                      π            ⁡                          [                                                (                                      3                    ⁢                                                                                            (                          7.5                          )                                                2                                            /                      2                                                        )                                +                                  3                  ⁢                                                            (                      1.7                      )                                        2                                                  +                                  3                  ·                  7.5                  ·                  1.7                                +                                                      (                    1.5                    )                                    2                                            ]                                                              =                ⁢                  0.25          ·                      3.14            ⁡                          [                                                1.5                  ·                  56.25                                +                                  3                  ·                  2.89                                +                38.25                +                2.25                            ]                                                              =                ⁢                  0.785          ⁡                      [                          84.375              +              8.67              +              38.25              +              2.25                        ]                                                  =                ⁢                              0.785            ⁡                          [              133.545              ]                                =                      104.83            ⁢                                                  ⁢            cubic            ⁢                                                  ⁢            inches                              
It would be desirable to have a speaker or passive radiator design where the outer diameter of the speaker cone is at least the diameter of the enclosure opening to which the acoustic radiator is mounted. Such an acoustic radiator design will provide several advantages. Some of the desired advantages are: a smaller enclosure for the same capacity acoustic radiator when compared to conventional speakers; the surround will not compromise the performance of the acoustic radiator; displacement of a greater volume of air with an enclosure opening that is the same size as a conventional speaker; and many others. The present invention provides such an acoustic radiator design.